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Scandinavian Workshop on Algorithm Theory

SWAT 2008: Algorithm Theory – SWAT 2008 pp 355–366Cite as

A Simple Linear Time Algorithm for the Isomorphism Problem on Proper Circular-Arc Graphs

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5124))

Abstract

A circular-arc model \( {\mathcal {M}} =(C,\mathcal{A})\) is a circle C together with a collection \(\mathcal{A}\) of arcs of C. If no arc is contained in any other then \(\mathcal{M}\) is a proper circular-arc model, and if some point of C is not covered by any arc then \({\mathcal{M}}\) is an interval model. A (proper) (interval) circular-arc graph is the intersection graph of a (proper) (interval) circular-arc model. Circular-arc graphs and their subclasses have been the object of a great deal of attention in the literature. Linear time recognition algorithms have been described both for the general class and for some of its subclasses. For the isomorphism problem, there exists a polynomial time algorithm for the general case, and a linear time algorithm for interval graphs. In this work we develop a linear time algorithm for the isomorphism problem in proper circular-arc graphs, based on uniquely encoding a proper circular-arc model. Our method relies on results about uniqueness of certain PCA models, developed by Deng, Hell and Huang in [6]. The algorithm is easy to code and uses only basic tools available in almost every programming language.

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Author information

Authors and Affiliations

  1. Facultad de Ciencias Exactas y Naturales, Departamento de Computación, Universidad de Buenos Aires, Buenos Aires, Argentina

    Min Chih Lin & Francisco J. Soulignac

  2. Instituto de Matemática, NCE and COPPE, Universidade Federal do Rio de Janeiro, Caixa Postal 2324, 20001-970, Rio de Janeiro, RJ, Brasil

    Jayme L. Szwarcfiter

Authors
  1. Min Chih Lin
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  2. Francisco J. Soulignac
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  3. Jayme L. Szwarcfiter
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Joachim Gudmundsson

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Lin, M.C., Soulignac, F.J., Szwarcfiter, J.L. (2008). A Simple Linear Time Algorithm for the Isomorphism Problem on Proper Circular-Arc Graphs. In: Gudmundsson, J. (eds) Algorithm Theory – SWAT 2008. SWAT 2008. Lecture Notes in Computer Science, vol 5124. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-69903-3_32

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  • DOI: https://doi.org/10.1007/978-3-540-69903-3_32

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-69900-2

  • Online ISBN: 978-3-540-69903-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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